Lemma 1 (Bounded Difference Inequality)  [1]}
Assume that \(Z= f(X_1,\cdots ,X_n)\) , with \(X_i\) s being independent, satisfies the bounded difference property with constants \(c_1,c_2,\cdots ,c_n\) . Denote
\(v = \frac{1}{4}\sum _{i=1}^n c_i^2\) 
